Occupational Licensing and Quality:

Distributional and Heterogeneous Effects in the Teaching

Profession

Bradley Larsen

Stanford University and NBER

May 14, 2015

Abstract

This paper examines a common form of entry restriction: occupational licensing. The paper stud-

ies two questions: first, how occupational licensing laws affect the distribution of quality, and second,

how the effects of licensing on quality vary across regions of differing income levels. The paper uses

variation in state licensing requirements for teachers and two national datasets on teacher qualifica-

tions and student outcomes from 1983–2008. Two measures of quality are used: the qualifications of

candidates entering the occupation (input quality) and the quality of service provided (output qual-

ity). Results show that more restrictive licensing laws—in the form of certification tests required for

initial licensure—may lead some first-year teachers of high input quality to opt out of the occupation.

In the sample of teachers who remain in the occupation multiple years, stricter licensing appears to

increase input quality at most quantiles of the teacher quality distribution. Output quality, as mea-

sured by student test scores, also changes with stricter occupational licensing, revealing a widening

of the distribution. For most forms of licensing studied, input and output quality improvements due

to stricter licensing requirements occur in high-income rather than low-income school districts.

Keywords: Occupational licensing, entry restrictions, quality, teacher certification

JEL Classification: J4, L5, K2, I2, L8

I would like to thank Mike Abito, Josh Angrist, Panle Jia Barwick, Sarah Cohodes, Jon Guryan, Caroline Hoxby, Sally

Hudson, Lisa Kahn, Morris Kleiner, Katie Larsen, Christopher Palmer, John Tyler, Chris Walters, and Frank Wolak, as

well as seminar participants at Brown University, the 2014 International Industrial Organization Conference, MIT, the 2015

NBER Law and Economics Winter Meetings, and the U.S. Department of Labor Employment and Training Administration,

for helpful comments and suggestions. I would also like to thank Josh Angrist and Jon Guryan for data help. This paper

has been funded, either wholly or in part, with Federal funds from the U.S. Department of Labor under contract number

DOLJ111A21738. The contents of this publication do not necessarily reflect the views or policies of the Department of

Labor, nor does mention of trade names, commercial products, or organizations imply endorsement of same by the U.S.

Government.

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1 Introduction

Occupational licensing affects nearly 30% of the US labor force (Kleiner and Krueger 2010), a larger

proportion of workers than are in unions or covered by minimum wage laws, and over 800 occupations

are licensed in at least one state ( Kleiner 2006). Doctors, lawyers, teachers, barbers, and, in some states,

even interior designers, auctioneers, frog farmers, fortune tellers, and florists, are required to have a license

to legally practice. Proponents of licensing argue that these laws decrease informational asymmetries by

preventing unqualified candidates from practicing, thus raising the lower tail of the quality distribution,

providing a minimum guaranteed level of quality and safety to consumers. 1 Opponents argue that

licensing merely secures higher rents for those in the occupation, raising prices and, in particular, harming

low-income consumers who may not be able to afford their preferred level of service. These debates date

back centuries and continue today.2

While studies have shown that licensing raises wages, raises prices for consumers, and deters entry,

little is known about the effects of licensing laws on the distribution of quality or about how licensing laws

differentially affect consumers of low vs high income. Section 2 discusses the existing empirical literature

of the effects of occupational licensing on quality, which have focused on average quality for the average

consumer, finding, for the most part, that licensing has no significant positive effect. However, from

a public interest standpoint, occupational licensing is intended to eliminate the worst candidates from

entering into an occupation (regulating input quality) or to prevent the worst outcomes from occurring

(regulating output quality).3 Therefore, in this paper I argue that effects on average quality may mask

important effects of licensing. In particular, licensing may have little effect on average quality but still

move the tails of the quality distribution. Moreover, price increases from occupational licensing may more

negatively impact low-income consumers than high-income consumers. Section 2 discusses theoretical and

1Many proponents present consumer safety as an argument for licensing. Ballou and Podgursky (1998) explain, “The [

professional teacher organization] frequently resorts to argument by analogy, comparing teaching to medicine...Doctors put

in years of training in medical school and residencies before achieving full professional standing. They must pass rigorous

licensing examinations. Why should we expect less of teachers?” Such arguments are frequently used in other professions as

well, such as in the recent Florida case, where interior designers, lobbying against a bill that would have de-regulated their

occupation by no longer requiring licenses, argued that the actions of unlicensed designers would lead to furniture in jail

cells being used as weapons, hospital fabrics spreading disease, and flammable rugs spreading fires, “contributing to 88,000

deaths every year” (Campo-Flores 2011). The interior designer lobby won the debate and the profession remains licensed

in Florida. Other proposals in Florida at this same time to deregulate other occupations, such as auctioneers, failed as well.2Adam Smith (1776) criticized the occupational licensing regimes of his time, and a recent Wall Street Journal article

highlighted that the Obama administration has budgeted $15 million to study the costs and benefits of occupational licensing

(Litan 2015).3This terminology distinguishing between input and output quality follows Shapiro (1986).

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qualitative studies which have touched on these issues—Leland (1979) and Arrow (1963) presented models

where licensing affects the distribution of quality, and Shapiro (1986) and Friedman and Friedman (1962)

highlighted that licensing may differentially affect low vs. high-income consumers—but these issues have

received little empirical attention. This paper is a first attempt to answer these questions empirically.

I focus on licensing in the market for teachers, using manually collected data on 26 years of state

requirements for teachers (1983–2008) and two national datasets on teacher qualifications and student

outcomes. Section 3 describes this data in detail, along with historical background about teacher certi-

fication tests. The measures of licensing stringency I employ are indicators for whether a given state in

a given year required teachers to pass certain certification tests (basic skills tests, subject tests, and pro-

fessional knowledge tests) prior to initial licensure.4 Teacher qualifications are measured by the strength

of teacher’s undergraduate institution using data on 60,000 teachers in the Schools and Staffing Survey

(SASS), serving as a measure of input quality, or the quality of candidates entering the occupation. Stu-

dent outcomes are measured by eighth grade math scores from over 300,000 students administered the

National Assessment for Education Progress (NAEP) exam, and serve as a measure of output quality, or

the quality of the service provided.

The teaching profession provides a useful setting for studying the effects of licensing for several reasons.

First, as described in Section 3, teacher licensing laws have been a major focus of public policy debates

in recent years (see recent Wall Street Journal article by Mehta 2013; see also Nadler and Peterson

2009 and Weddle 2014) and in the past (Darling-Hammond 1997; Ballou and Podgursky 1998; Gardner

1983). Second, I observe measures of quality, which is rare in other occupations (Kleiner 2006; Gross

1986). Third, the use of licensing test laws varied greatly across states and across time from 1983–2008,

allowing for identification of the effects of this particular form of licensing. Fourth, teacher certification

tests represent a real obstacle to some candidates.5 Also, these certification tests must be passed prior

to initial licensure for teachers seeking standard certification and, in most states, for teachers seeking

alternative certification, making it simple to identify which subgroup of teachers were affected by law

4In much of the occupational licensing literature (Kleiner 2006), the term “licensing” refers to mandatory requirements

that must be met in order to legally practice in the profession, while “certification” refers to a qualification that a professional

may obtain but which is not required in order to legally practice. Given that in the teaching profession licensing exams are

referred to as “certification” exams, I use the both terms to refer mandatory requirements.5The nationwide pass rate was 76% for whites and 42% for non-whites in 1984 (Rudner 1987), 93% in 2000 (Paige,

Sroup, and Andrade 2002), and 96% in 2006 (Duncan and Ochoa 2002). Note that the test could be a costly obstacle to

some even if the reported pass rate were 100%, as this pass rate is an equilibrium outcome of test difficulty and candidates’

preparation effort. Further evidence that certification tests are a challenge to at least some candidates is found in the fact

that test preparation companies offer numerous study products to aid students in preparing for the Praxis exams, the set

of exams used by most states today.

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changes.6 Finally, certification test laws are easily quantifiable. Coursework or degree requirements, while

potentially more costly to candidates than certification tests, are difficult to translate into a measure of

licensing stringency.

Section 4 presents the empirical approach. To estimate the effects of certification test laws on the

distribution of quality, I adopt the grouped quantile regression approach of Chetverikov, Larsen, and

Palmer (2015), a quantile extension of Hausman and Taylor (1981). This approach allows me to focus

on the effects of licensing on quantiles of the quality distribution rather than simply on average quality.

To estimate how occupational licensing laws differentially affects average quality in high vs. low-income

areas, I interact measures of licensing stringency with the percent of students qualifying for free lunch.

I compute these effects for measures of input and output quality, and do so both for first-year teachers

alone as well as for a pooled sample of new and experienced teachers, allowing me to form a synthetic

panel that exploits additional variation in state licensing requirements.

In Section 5 I present the findings of the paper: an analysis of how certification test requirements

for teachers affect the distributions of input and output quality, and how the effects of these laws differ

for high vs. low-income areas. When examining the input quality distribution for first-year teachers, I

find that subject area certification tests for initial licensure lowered the upper tail of the input quality

distribution, suggestive that these licensing requirements may have driven away from teaching some

candidates coming from highly selective undergraduate institutions. When instead examining long-run

effects (i.e., looking at experienced teachers), I find that the effects of subject test laws are positive and

relatively constant across the distribution of quality. In examining output quality, I find that, for first-year

teachers, certain certification tests are associated with a decrease in the lower tail and an increase in the

upper tail of the distribution of output quality, suggesting that the student test score distribution widens

under stricter licensing requirements.

In examining how licensing requirements differentially affect areas of high vs. low-income, I find

that any positive effects of teacher certification tests on quality accrue primarily to higher-income school

districts. This is true for both input and output quality effects for most types of teacher certification tests.

I also find some weak evidence that when certification tests are in place, lower-income school districts

may substitute away from hiring licensed professionals by instead hiring emergency-certified teachers or

increasing class sizes. Finally, I perform an event study that suggests that the primary impact of subject

6This is not the case with other licensing requirements, such as specific coursework requirements or a requirement to

have a master’s degree within a certain number of years, which differ by state and by whether or not the teacher was

regularly or alternatively certified; in some states, a change in such laws would affect a potential teacher after completing a

bachelor’s degree, while in others, a change in requirements would affect the candidate midway through an undergraduate

program.

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test laws on quality occurs two or more years after the change in certification requirements, consistent

with the existence of phase-in periods for these regulatory changes or with undergraduate major choices

being influences by these changes.

Finally, Section 6 concludes and offers several suggestions for future research in occupational licensing

to continue moving beyond studying average quality.

2 Theoretical and empirical work on occupational licensing

This section provides a brief discussion of previous theoretical and empirical work on occupational li-

censing, in particular in relation to the effects of licensing on the quality distribution and the differential

effects of licensing for high and low-income consumers. Leland (1979) presented a model in the spirit

of the lemons model of Akerlof (1970) in which licensing can weed out low-quality candidates from the

occupation. Arrow (1963) provides a similar qualitative discussion. Shapiro (1986) presented a model

in which licensing can encourage professionals to invest in producing higher quality services, as licensing

laws provide an assurance to professionals that they will be able to reap the benefits of such investment.

On the other hand, arguments such as those in Stigler (1971) and Peltzman (1976) suggest that licens-

ing may decrease competition, which could lead to lower quality. Leland (1979) also pointed out that

licensing standards set by industry organizations, as many are, will likely be set too high in an effort

to increase market power. In addition, Ballou and Podgursky (1998) and other opponents of licensing

argued that increasing licensing stringency may lead to a decrease in the upper tail of quality if the costs

(monetary or time costs) of licensure induce candidates with higher outside opportunities to choose a

different career.

The preceding literature is entirely theoretical; previous empirical research on occupational licensing

has largely ignored the effects of licensing on the distribution of quality, instead focusing on average

quality. Kleiner and Petree (1988), Berger and Toma (1994), Hanushek and Pace (1995), Goldhaber and

Brewer (2000), Rockoff, Jacob, Kane, and Staiger (2008), Kane, Rockoff, and Staiger (2008), and Angrist

and Guryan (2008, 2004), all focused on average effects and found no effect or a negative effect of increased

licensing stringency on standardized test scores for students, the selectivity of teachers’ undergraduate

institutions, or other measures of teacher quality. Studies have also found non-positive effects of licensing

on quality for electricians (Carroll and Gaston 1981), contractors (Maurizi 1980a), dentists (Kleiner and

Kudrle 2000; Carroll and Gaston 1981), and physicians (Kugler and Sauer 2005).

Figure 1 illustrates effects that would be missed by examining only average quality. In panel (a),

licensing leads to an increase in quality in the lower tail of the distribution. In (b) quality increases at

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every quantile of the distribution. Focusing solely on average quality would not enable one to disentangle

whether licensing serves only to drive out low-quality services or instead improves service across the

board. Similarly, average quality decreases in both panels (c) and (d), but in (c) the decrease occurs

primarily in the upper tail, driving out high-quality services and in (d) quality decreases at all quantiles.

The results in Wiswall (2007) and Sass (2011) for teachers and in Ramseyer and Rasmusen (2015) for

lawyers can be interpreted as evidence consistent with panel (c). Perhaps the most interesting case is (e),

where licensing increases the lower tail, as suggested is possible in the Leland (1979) model, for example,

and simultaneously drives out high-quality, high-outside-option candidates, as suggested by Ballou and

Podgursky (1998), leading to a zero effect on average quality. Panel (f) provides a similar illustration

with a mean-preserving spreading of the distribution rather than condensing.

Understanding which portion of the quality distribution is affected is key to understanding several

policy issues: first, it can aid in understanding whether occupational licensing has any impact at all on

quality (such as increasing the lower tail, even without moving the average); and, second, if licensing does

have an effect, such analysis can aid in determining whether the benefits of licensing outweigh its costs,

or whether alternative forms of quality improvement would be preferred, such as reputation systems or

non-mandatory certification systems, such as those suggested by Shapiro (1986) and Kleiner (2006).

The differential effects of occupational licensing on consumers who differ by income or preference for

quality were highlighted in the theoretical model of Shapiro (1986), who suggested that any benefits of

licensing will accrue primarily to those consumers with a greater preference toward quality, benefiting

high-income consumers at the expense of low-income consumers. Friedman and Friedman (1962) made

a similar point, suggesting that licensing laws may prevent low-income consumers from gaining access to

the service due to a lack of low-quality or lower-priced services. Currie and Hotz (2004) found empirical

evidence of this effect, demonstrating that tighter educational requirements for child care professionals

led to higher quality for children who received care, but also led to price increases resulting in less children

being served. Also, Kleiner (2006) found that more restrictive licensing requirements in dentistry tended

to benefit high income states and had no effect on low-income states. However, the majority of the

empirical occupational licensing literature has not examined these heterogeneous effects for high vs. low-

income consumers. It may be that the zero average effects documented in previous studies (described in

the above paragraphs) mask underlying positive effects for high-income consumers and negative effects for

low-income consumers, as theory suggests. This concept is illustrated in panel (a) of Figure 2, where the

dashed line represents the average effect of increasing licensing stringency and the solid line represents the

effect at different income levels (or different levels of the percent of students qualifying for free lunch).

Panel (b) illustrates the opposite phenomenon, where the effect of licensing is larger for low-income

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(high percent free lunch) areas. The interaction effects studied below provide a test of whether licensing

differentially affects these different areas.7

3 Background and data on teacher certification laws and quality

measures

3.1 Teacher certification laws

Competency tests for teachers were used in many states in the early twentieth century (Rudner 1987).

Over time, testing requirements were replaced by educational requirements for prospective teachers, such

as a bachelor’s degree or specific education coursework. In the late 1970s and early 1980s, states devel-

oped a renewed interest in teacher testing, sparked by professional organizations, such as the American

Association of Colleges for Teacher Education (AACTE), and by the influential report, “A Nation at

Risk,” (Gardner 1983) commissioned by the Department of Education, which advocated for educational

reform, arguing that education professionals too often came from the bottom quartile of high school

graduates.

As certification tests became more widespread from the 1980s to today, they evolved into three

categories: basic skills tests (testing listening, reading, writing, communication, and mathematics), pro-

fessional knowledge tests (testing pedagogical skills and knowledge), and subject matter tests (testing

specific subjects).8 Figure 3 displays the proportion of states requiring each type of certification test

during the years 1983 to 2010.9 I manually compiled data on teacher certification test laws from the

following teacher certification manuals, which list historical details of certification requirements for each

state: AACTE (1990, 1991, 1993–1996), Boydston (1995-1999, 2001–2010), Coley and Goertz (1990),

Goddard (1983–1993), Goertz (1986, 1988), NASDTEC (1991, 1994, 1996, 1996, 2000–2002), NASDTEC

Knowledgebase (2003–2010), Neuweiler (1988), Rudner (1987).

7Other aspects of occupational licensing examined in the empirical literature, and not focused on in this paper are

effects on minority participation in the profession (Federman, Harrington, and Krynski 2006; Law and Marks 2009) and

wages (Maurizi 1980b; Kleiner and Petree 1988; Kleiner 2000; Kleiner and Kudrle 2000; Tenn 2001; Kugler and Sauer 2005;

Angrist and Guryan 2008; the large majority of these studies found positive effects on wages).8For elementary school teachers, subject matter exams test content specific to teaching younger children. Also, some

tests are referred to as general knowledge tests, and can include general knowledge of social studies, math, literature, fine

arts, and science. However, in the historical certification manuals I use, both general knowledge tests and basic skills tests

are often referred to as basic skills tests, and are thus indistinguishable. Therefore, I treat both as basic skills tests.9The main empirical analysis of the paper uses only years 1983–2008 because quality measures are not available for

2009–2010.

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As shown in Figure 3, by the late 1980s most states required some form of teacher testing. In

the late 1990s, professional teacher organizations, such as the National Commission on Teaching and

America’s Future (NCTAF), the National Council of Accreditation of Teacher Education (NCATE), and

the National Board for Professional Teaching Standards (NBPTS), argued for even stricter certification

requirements (NCTAF 1996). Opponents of this movement argued that increasing the restrictiveness of

licensing requirements would only drive away more qualified applicants with higher opportunity costs,

inducing them to turn down teaching for alternative careers (Ballou and Podgursky 1998).

In the most recent decade, as seen in Figure 3, the use of basic skills tests and professional knowledge

tests decreased, and the use of subject matter tests increased, in part due to the No Child Left Behind

Act of 2001. A portion of this legislation required that, by the end of the 2005-2006 school year, each state

demonstrate that its teachers met the definition of a Highly Qualified Teacher (HQT), which included

demonstrating subject matter competency (Kuenzi 2009). Table 1 displays the number of states (including

Washington, D.C.) that experienced a change from having no subject test law to having a subject test

law, or vice-verse, and similarly for the other types of tests. Notice that very few states (only two)

experienced a change from having a subject test law to having none. I exploit this fact in the analysis

below to perform an event study of the impact of licensing changes.

3.2 Input and output quality measures

I measure input quality (i.e. a candidate’s qualifications) using the selectivity of the teacher’s under-

graduate institution. I begin with data on public school teachers from the Schools and Staffing Survey

(SASS) from the US Department of Education’s National Center for Education Statistics (NCES).10 The

SASS survey was administered in years 1988, 1994, 2000, 2004, and 2008 to a nationally representative

sample of teachers.11 The dataset provides information about the school district in which a teacher is

employed, such as the percent of students eligible for free school lunch, which serves as a measure of the

income level of the district. The data also contains information about individual teachers, such as their

years of teaching experience, the state in which they teach, and their undergraduate institution. The

undergraduate institution is recorded as a Federal Interagency Committee on Education (FICE) code,

10Public versions of SASS are available at nces.gov. I use the restricted-use SASS sample, which allows me to link

teachers to their undergraduate institution. The restricted-use data is available in a secure fashion to researchers who apply

for access through nces.ed.gov/pubsearch/licenses.asp. In compliance with NCES disclosure requirements, all sample sizes

from raw NCES data reported herein are rounded to the nearest 10.11These numbers refer to the year the school year ended. I follow the same convention throughout the paper. An

additional SASS survey was administered in 1991 but did not contain information on teachers’ undergraduate institutions,

and thus is omitted from the analysis except in the regressions in Section 5.5 examining substitution effects, where I use

other dependent variables (salary and emergency certification) found in the SASS survey.

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which I merge with data on the average SAT score of entering freshmen for the undergraduate institution

of the teacher, from a survey conducted by the Higher Education Research Institute (see Astin, Green,

Korn, and Maier (1983) and the description in Angrist and Guryan (2008)). A single observation in the

SASS data represents a particular teacher and the selectivity of that teacher’s undergraduate institution,

which I then link to state certification test laws for initial licensure for the specific year in which the

teacher was certified. I then treat this observation as an independent draw from the teacher input quality

distribution in a given year and state.12

Summary statistics for the main variables of interest from the SASS dataset are displayed in Table

2. The mean and standard deviation of the teacher input quality measure are 916 and 107 SAT points,

respectively. In the analysis performed below, I standardize this quality measure so it has mean zero and

variance one within the sample, meaning all quality results are reported in terms of standard deviations.

I limit the sample to teachers with less than 12 years of experience. I refer to the years in which the SASS

survey was administered as survey years. In the analysis below, I group together teachers whom I observe

in the same state and year and of the same experience level, and I refer to this group as a cohort. For

example, a teacher who began teaching in the 1992-1993 school year and who was surveyed in 1993-1994

school year would be in the cohort of teachers with two years of experience. I drop cohorts with fewer

than ten teachers recorded. Table 2 shows that the number of teachers in a state-year-experience level

cohort, described below, ranges from 10 to 113, with a mean of 33. The percent of students in the school

district eligible for free lunch is 39% on average. Summary statistics for other covariates from the SASS

dataset are reported in Appendix Table A.1.

To measure output quality I use public school student test scores from the eighth grade math National

Assessment of Educational Progress (NAEP) exam from the NCES.13 The test was administered in 1990,

1992, 1996, 2000, 2003, 2005, and 2007. The NAEP data contains information on student test scores and

other covariates, as well as information on each student’s teacher.14 A single observation in the NAEP

12Measuring quality in any occupation is difficult, and a source of debate among researchers (Gross 1986). Similar

measures of quality to that which I use have been used in Bacolod (2007), Kane and Staiger (2008), Hoxby and Leigh

(2004), Figlio (1997), and Angrist and Guryan (2008, 2004). This input quality measure is not meant to capture everything

about an individual teacher’s qualifications; instead, it is meant to serve as some measure of the impressiveness of a

candidate’s resume to employers when the candidate enters the job market. It is reasonable to assume that the selectivity

of a teacher’s undergraduate institution is correlated with the prestige of the teacher’s resume.13Public versions of NAEP are available at nces.gov. I use the restricted-use NAEP sample, which allows me to link

each student to the number of years of experience of the student’s teacher. The restricted-use data is available in a secure

fashion to researchers who apply for access through nces.ed.gov/pubsearch/licenses.asp.14The data does not record raw test scores for students, but rather reports five plausible scores calculated using student

responses and item response theory (IRT). As explained in Kolstad (2006), these five scores in the NAEP data represent

independent draws from the posterior distribution of scores for students with similar item response patterns and similar

9

data represents a student test score, which I link to state certification test laws for initial licensure for the

specific year in which the student’s teacher was certified. I then treat this observation as an independent

draw from the output quality distribution in a given year and state.15

Summary statistics are displayed in the lower half of Table 2. Observe that student scores on the

NAEP eighth grade math exam are 262 on average, with a standard deviation of 39. As with input

quality, in the analysis below, I standardize these test scores to have mean zero and variance one within

the sample, so all results are reported in standard deviation units. As with the SASS survey, I refer to

years in which the NAEP test was administered as survey years, and to students being taught by teachers

of a given experience level as a cohort. For example, students who were tested in 1994 and who were

taught by a teacher who began teaching in the school year ending in 1993 would be in the cohort of

students taught by teachers with two years of experience. I drop cohorts with fewer than ten students

recorded. The number of students in each state-year-experience cohort ranges from 10 to 1,439, with a

mean of 203. The NAEP data also contains the percent of students eligible for free lunch, reported in

bins rather than as continuous variables. A school is classified as having either 0–5%, 6–10%, 11–25%,

26–50%, 51–75%, or 76–100% of its students qualifying for free lunch, and the distribution (not shown)

is roughly uniform across quartiles. Summary statistics for other variables from the NAEP dataset are

found in Appendix Table A.1.

It is impossible to link the SASS and NAEP datasets. This is less problematic in this study than in

other contexts, however, because I do not wish to derive a link between input and output quality or to

estimate an education production function (Hanushek 1979). Instead, the focus of this study is simply

to determine whether or not teacher certification tests have any detectable effect on the distribution of

quality—either for input or output quality—and whether average quality effects differ for high vs. low

income areas.

I use one additional data source in the regressions in Section 5.5 studying the effects of teacher

certification laws on pupil to teacher ratios. This dataset comes from the NCES Common Core of Data

observable characteristics. I take the average of the five IRT draws, as in Fryer (2011), and treat this as an output quality

draw. See also Jacob (2007) for a discussion.15To measure output quality, it would be desirable to translate student test scores into a measure of teacher value-added

by aggregating to the teacher level, as in Kane and Staiger (2008), for example. However, NAEP survey designers claim

that the survey is not representative at the teacher level and warn against aggregating to the teacher level (Rogers and

Stoeckel 2008). Also, in many cases very few students assigned to a particular teacher appear in the dataset. Finally, as

the data is in the form of a repeated cross-section rather than a panel, no baseline measure of student ability is available,

which Kane and Staiger (2008) show greatly increases the explanatory power of teacher value-added measures. Therefore,

I focus on the distribution of student test scores rather than teacher value-added, and treat each realization of an NAEP

test score as a draw from the output quality distribution.

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(CCD) from 1987–2010 and is available publicly on the NCES website. Summary statistics are found in

Appendix Table A.1.

4 Estimating distributional and heterogeneous effects

In this section I present several approaches to identifying the effect of teacher certification tests on

quality. To clarify the estimation approach, I focus first on the input quality distribution for first-

year teachers and then expand the approach to incorporate other levels of experience. I then explain

the approach for estimating the effects on the output quality distribution and then the approach for

identifying heterogeneous effects of licensing requirements on quality differing by income level.

4.1 Estimating distributional effects of teacher licensing requirements

I focus first on the case of first-year teachers. Recall that the SASS and NAEP were only administered

in certain years, and hence records for first-year teachers include only those teachers who began their

career during a survey year. Recall also that teacher input quality corresponds to the selectivity of the

teacher’s undergraduate institution (as measured by the averaged SAT score of entering freshmen). For a

fixed τ ∈ (0, 1), let qτst be the τ th quantile of teacher input quality within state s for teachers who began

teaching in year t, which I model as

qτst = γs(τ) + λt(τ) + Law′stδ(τ) + εst(τ) (1)

where γs(τ) is a state effect and λt(τ) is a year effect. State effects capture characteristics that are

unchanging over time within a state (e.g., some states may have higher quality teachers than others over

the entire sample period). Year effects capture factors that affect every state in a given year (e.g., in

2005, No Child Left Behind legislation affected all states by mandating that each state specify a method

for ensuring competence in teachers’ subject areas). Lawst is a three-element vector containing dummies

equal to 1 if a subject test, basic skills test, or professional knowledge test was required in state s in

year t. δ(τ), the parameter vector of interest, represents the effect of teacher certification test laws on

the teacher input quality distribution. A positive value of δ(τ) at τ = 0.1, for example, would indicate

that these occupational licensing laws increase the lower tail of input quality, barring some less-qualified

candidates from the occupation. The final term, εst(τ), represents unobserved factors at the state-year

level which can affect the τ th quantile of quality in state s and year t.

The identifying assumption of this model is that unobserved state-year specific factors εst(τ) are un-

correlated with the incidence of state certification laws. This assumption would be violated, for example,

11

if changes in state certification requirements were imposed at the same time as other state-specific policies

which also affected the teacher quality distribution. While it is impossible to rule out all possible such

unobservables, Angrist and Guryan (2008), examining average effects rather than quantile effects, argue

that this exogeneity assumption is reasonable in this setting given that actual licensing requirements and

hiring decisions are made at the school district level, not the state level, and districts often enforce a

stricter standard than the state requirements, such as requiring teacher testing even when not mandated

by the state.16

The quantile-based model in (1) is a special case of the general grouped instrumental variables quantile

model presented in Chetverikov, Larsen, and Palmer (2015), and I apply here the estimator proposed

therein. The grouped quantile estimator represents an extension of the Hausman and Taylor (1981)

estimator to quantile regression settings and can be performed in this case by simply computing the τ

quantile of teacher input quality within each state-by-year cell (a “group”) and treating this computed

quantile as the dependent variable in an OLS regression, with one observation per group, to estimate

model (1). Standard quantile regression (Koenker and Bassett 1978) would be inconsistent in this setting

given the existence of group-level unobservables, εst.17 This approach also has computational advantages

over standard quantile regression, which can be quite slow and often fail to converge in standard statistical

packages when many right-hand-side variables are included, such as the state and year effects in (1). The

grouped quantile approach, on the other hand, handles any group-level right-hand-side variables through

a simple OLS regression, greatly reducing computation times.18

One robustness test of (1) can be performed by including state-specific linear time trends, yielding

the following model:

qτst = γs0(τ) + γs1(τ)t+ λt(τ) + Law′stδ(τ) + εst(τ) (2)

16Angrist and Guryan (2008) regress average teacher quality within a school-district-by-year cell on state-by-year-level

requirements, arguing that this state-by-year variation in licensing laws serves as a valid instrument for district-by-year-level

requirements, thus treating this state-by-year variation as exogenous, as in this paper.17The standard quantile regression model of Koenker and Bassett (1978) solves the following problem for a given τ :

min(γs(τ),λt(τ),δ(τ))

∑i

ρτ(qist − γs(τ)− λt(τ)− Law′

stδ(τ)),

where qist represents the individual-level data on teacher i in state s in year t and where ρτ (·) is a “check” function of

Koenker and Bassett (1978), i.e. ρτ (x) = (u − I{x < 0})x. Unlike the grouped quantile approach, standard quantile

regression does not allow for additively-separable group-level unobservables (εst(τ)) and such unobservables would lead to

inconsistency of the standard quantile regression estimator (see Hausman 2001).18I also estimated the standard quantile regression analog of (1) (i.e., assuming εst(τ) = 0) and found it to be more than

100 times slower than the grouped approach.

12

Equation (2) controls for unobserved factors that may affect the quality distribution within a state and

that change continuously over time. If equation (1) is well identified, one would expect similar estimates

of the effects of licensing on quality from (1) and from (2).

To incorporate data from other experience cohorts, I modify (1) by writing the τ th quantile of input

quality of teachers in state s who had c years of experience when they were surveyed in survey year t as

qτstc = γs(τ) + λt(τ) + αc(τ) + Law′stδ(τ) + εstc(τ) (3)

where γs and λt are as above, and αc represents a cohort fixed effect. Lawstc is a three-element vector

containing dummies equal to 1 if a subject test, basic skills test, or professional knowledge test was

required in state s for teachers surveyed in year t belonging to cohort c when these teachers were initially

licensed. Therefore, the test law dummies correspond to the year in which the teacher cohort would have

received initial certification. The term εstc(τ) represents unobserved factors at the state-year-experience

cohort level that affect the distribution of teacher input quality. Grouping cohorts in this fashion and

pooling the data together in estimation forms a “synthetic panel” or “pseudo panel” (see Verbeek and

Nijman 1992 or Deaton 1985).

One concern with pooling all experience cohorts is that the experienced teachers, for example, those

with five years of experience, who are present in survey year t consist of a group which has self-selected

to remain in the profession five years. This is not a problem if the experience/cohort effect does not differ

by state, because this effect is controlled for by αc. However, if the effect of experience on quality differs

by state, and if this effect is related to policy changes occurring simultaneously with changes in teacher

certification requirements, ordinary least squares estimates of δ would be biased. One specification check

I employ in Section 5 below is to replace αc above with state-specific returns to experience, αc + αsc,

similar to the state-specific linear time trends in (2).

The model in (1) above can be modified to estimate the effect of teacher certification laws on the

distribution of output quality (student test scores from the NAEP) by letting qτst be the τ th quantile of

the student test score distribution among students taught by teachers who began teaching in state s and

survey year t. Equation (3) is similarly modified, with the qτstc being the τ th quantile of the student test

score distribution among students taught by teachers with c years of experience in state s and survey

year t. Therefore, for students appearing in the NAEP sample in survey year t taught by cohort c in state

s, the certification test law indicators correspond to the year in which the teaching cohort that taught

these students would have received their initial certification.

In the results discussed below in Section 5, some specifications also include an additional vector of

state-year observable covariates, Xst, including student enrollment; the percent of students eligible for

free lunch; the percent minority enrollment; the proportion of the state categorized as suburban, city,

13

or rural; and a quadratic term in the state unemployment rate. Output quality regression models also

include the percentage of students who report having an encyclopedia in the home as a simple control

for students’ educational environment at home.

4.2 Estimating heterogeneous effects by income

To estimate the effect of occupational licensing on average quality for school districts of differing income

levels, I estimate regressions of quality on an interaction term of test law dummies with the percent of

students qualifying for free lunch. These regressions are of the following form:

qidst = γs + λt + Law′stδ + Lunchdst ∗ Law′stψ + Lunchdstξ + νidst (4)

where qidst is the input quality of teacher i in school district d in state s and survey year t. Lunchdst

represents the percent of students in district d, in state s, in survey year t who qualify for free school

lunch. Thus, a higher value of this variable represents a lower income school district. Unlike (1), the

regression in (4) is a model of the individual quality of teacher i, not of a group-level (state-by-year)

measure. Also, unlike (1), the regression in (4) is not a model of conditional quantiles, and hence all

unobserved heterogeneity is captured in the term νidst. Thus, ordinary least squares estimation of this

model measures the effect of stricter licensing requirements on average quality for areas of differing income.

In the case where all experience cohorts are pooled together, I modify (4) to include cohort effects as in

(3). The effect of teacher certification laws on the average input quality of teachers found in a school

district in which %I of students qualify for free lunch is given by δ + Iψ. The parameter ξ captures the

main effect of the percent of students qualifying for free lunch.

To examine heterogeneous effects on output quality, I replace qidst with the NAEP test score of student

i in school d in state s in survey year t.19 In the NAEP datasets, the percentage of students qualifying

for free lunch is not recorded as a continuous variable. Instead, discrete data are recorded, classifying the

school as having either 0–5%, 6–10%, 11–25%, 26–50%, 51–75%, or 76–100% of its students qualifying

for free lunch. Therefore, rather than containing an interaction with a single continuous variable, the

output quality regression is fully saturated with interactions between law dummies and percentage free

lunch dummies:

qidst = γs + λt +

6∑j=1

pjdst ∗ Law′stψj +

6∑j=1

pjdst ∗ ξj + νidst (5)

19In the NAEP, the percent free lunch variable is recorded at the school level, whereas in the SASS data it is recorded

at the district level.

14

where pjdst are dummies specifying which of the six free lunch categories contains school d in state s in

survey year t. The parameters ξj capture the main effect of the percent free lunch variables. A similar

modification yields the pooled cohorts specification.

As highlighted above, it is important to note that if unobserved factors at the group (state-by-year or

state-by-year-by-cohort) level are correlated with changes in teacher certification testing requirements,

each of the approaches described above will yield biased estimates of the effects of testing laws on

teacher quality. For example, other education policies may have changed simultaneously with teacher

certification requirements. If such policy changes did occur, and these policies are complements with

teacher certification testing, the measured effects could simply be interpreted as the total effect of the

policy changes rather than the specific portion of the effect attributable to certification tests. If, however,

unobserved policy changes and certification testing are substitutes, the estimated effects will be difficult

to interpret. While I am unable to rule out all possible confounds, below I check the robustness of the

results to the inclusion of time and experience trends and present an event study to explore whether the

timing of effects is consistent with the changes in licensing laws.

5 Results: The effects of licensing on the distribution of quality,

and differential effects of licensing by income level

In this section I present the results of the estimation procedure described in Section 4. I first present

the grouped quantile regression estimates of the effects of certification test laws on the distributions of

input quality (i.e. the selectivity of a teacher’s undergraduate institution as measured by the institution’s

average SAT score for entering freshmen) and output quality (student NAEP test scores). I then present

the estimates of the effects of certification testing on input and output quality in regions differing by

income level. Finally, I estimate the effects of licensing on outcomes other than quality to examine

whether certification tests lead low-income areas to substitute away from hiring licensed teachers.

5.1 The effects of licensing on input quality

5.1.1 Effects on average input quality

Before addressing the question of whether stricter occupational licensing laws lead to an increase in the

lower tail of the distribution of teacher input quality, I first estimate a regression of average teacher input

quality on teacher testing laws. The first three columns of Table 3 display the results of estimating (1), i.e.

using first-year teachers only, where the dependent variable is replaced with qst, the mean of input quality

15

in state s in survey year t. Column 1 includes only state and year effects, column 2 adds state-year level

demographic controls as explained above, and column 3 adds a state-specific linear time trend. Columns

4–6 repeat the exercise for the pooled sample of teachers. Column 7 adds a term capturing state-specific

returns to teacher experience, and column 8 includes both the time trend and the experience trend.

Columns 1–3 suggest that none of the test laws have a statistically significant impact on the average

input quality of first-year teachers, which is consistent with the results of Angrist and Guryan (2008).

However, because surveys occurred at 4–6 year intervals, estimation with only first-year teachers does not

take advantage of all historical variation in teacher certification test laws. The pooled sample of teachers,

on the other hand, uses all teacher cohorts, thus using a larger sample and using variation in certification

test laws over the entire period (1983–2008).

Column 4 indicates that subject test laws are associated with a statistically significant increase of 0.08

standard deviations in average teacher input quality among the pooled teachers sample. This suggests

that, controlling for years of teaching experience, teachers who remain in the occupation multiple years

and who were required to pass a subject test prior to initial licensure are more likely to come from highly

selective undergraduate institutions than those who did not face this requirement. The basic test law

and professional knowledge test laws do not have a significant effect. Columns 5–8 indicate that these

findings are robust to the inclusion of demographics, time trends, experience trends, or both.

5.1.2 Quantile effects for input quality

To examine how teacher certification laws affect the distribution of input quality, I estimate (1) separately

for each decile (τ = 0.1, 0.2, ..., 0.9) of teacher input quality. The results are shown in Figure 4. Panels

on the left of Figure 4 (i.e. (a), (c), and (e)) display the effects of subject, basic skills, and professional

knowledge test laws at each quantile using the sample of first-year teachers, and panels on the right (i.e.

(b),(d), and (f)) use the pooled sample of experienced teachers. All regressions include demographic

variables and state and year fixed effects, as in columns 2 and 5 of Table 3. Point-wise 90% confidence

intervals are represented in gray.

Estimation using the first-year teacher sample demonstrates a generally downward-sloping quality

effect for subject and basic skills tests, implying that, among first-year teachers, certification test laws

may have a more positive impact on the lower tail than on the upper tail of quality, although at most

quantiles the effect is not significant. For subject test laws, the decrease in the upper tail (the 0.8 quantile)

is statistically significant. This decrease in the upper tail of teacher input quality presents some evidence

in favor of the hypothesis of Ballou and Podgursky (1998) that occupational licensing can drive away

highly qualified candidates. Note that this effect is not possible to detect when looking only at effects

16

on average quality as in Table 3. Figure 4 does not show strong evidence of certification tests weeding

out less-qualified candidates, as the estimates for each sample and test type are not significantly positive

at lower quantiles, although the point estimate is positive for the basic skills test at the 0.1 quantile for

first-year teachers.

The pooled sample of teachers yields a significant effect of subject test laws on the distribution of

teacher qualifications, as shown in panel (b) and at some quantiles of panel (d) of Figure 4. The effect

of licensing is positive, implying that the sample of teachers who remain in the occupation for multiple

years is more likely to come from highly selective undergraduate institutions when subject test laws are in

place than when they are not. Interestingly, this result is relatively flat across the distribution, indicating

that subject test laws do not appear to differentially affect the lower tail of the distribution and upper

tail of the distribution. To examine the robustness of these results, Appendix Figure A.1 displays the

same results as in panel (b) of Figure 4, that is, the effect of subject test laws using the pooled sample of

teachers, but with time and experience trends included. The results do not change drastically with the

inclusion of these trends, consistent with treatment and control states not differing drastically in their

input quality trends prior to changes in licensing laws.

This finding for the pooled sample of teachers is in contrast to the Ballou and Podgursky (1998)

hypothesis and the results in panel (a) of Figure 4, which found a decrease in the upper tail of input

quality due to licensing among first-year teachers. Together, these results suggest that stricter licensing

requirements may drive away some highly qualified first-year teachers in the short run but have a positive

longer-run effect on the quality. That is, if licensing drives out high-quality first-year teachers, panel (b)

suggests that these teachers would likely not have remained in the occupation anyway.

5.2 The effects of licensing on output quality

5.2.1 Effects on average output quality

Before estimating the effects of occupational licensing on the distribution of output quality, I first estimate

(1) with the dependent variable being the average eighth grade math NAEP score within a given group

(state-by-year or state-by-year-by-cohort). The results are displayed in Table 4. For the pooled sample

columns, the dependent variable is the mean among students taught by teachers in cohort c in state s

in survey year t. Subject test laws appear to have no effect, while basic skills test laws appear to have

an effect of about 0.05 standard deviations, but this effect is not robust to the inclusion of time trends.

Professional knowledge test laws appear to have a small but imprecisely-measured negative effect. As a

useful benchmark, other interventions in education, such as the class size experiments of Krueger (1999),

have led to increases in student test scores of approximately 0.2 standard deviations.

17

5.2.2 Quantile effects for output quality

The effects on the distribution of output quality (NAEP student test scores) are displayed in Figure 5.

The grouped quantile approach makes it possible to study effects on the entire distribution, as advocated

by Brown and Saks (1975) and the ensuing literature, which recommended examining the variance of

student outcomes rather than simply the mean. As above, the results in Figure 5 come from estimating

(1) at each decile of output quality, controlling for demographics and state and year effects and, in the case

of the pooled sample, experience effects. Panel (a) demonstrates that, in the first-year teacher sample,

subject test laws are associated with a 0.15 standard deviation drop in the lower tail of the distribution.

The effect also appears to be increasing with the quantile. In the pooled sample, panel (b), the effect on

the lower tail is smaller and insignificant, but the increasing shape is preserved, and a positive impact

of 0.05 standard deviations is detected at the 0.9 quantile. Panels (c) and (d) demonstrate that basic

skills test laws increase test scores by 0.05–0.10 standard deviations across most of the distribution,

while panel (f) shows a marginally significant negative impact of 0.05 standard deviations for professional

knowledge test laws on the middle and far right quantiles. Overall, Figure 5 suggests that most of the

positive effects of these teacher certification tests accrue to the upper half of the distribution, implying

a widening of the student test score distribution. While is not obvious why this widening would occur,

one possibility is these certification tests screen teaching candidates on abilities best suited for providing

value to students who perform at or above the median—a question meriting further research. Neal and

Schanzenbach (2010) documented related results which suggest that educational interventions such as

changes in proficiency requirements may lead teachers to focus on students at certain points of the test

score distribution.

Appendix Figure A.2 checks the robustness of the effects of subject test laws and basic skills test

laws in the pooled sample. The subject test results remain similar even with the inclusion of experience

trends. The basic skills test results change shape somewhat when state specific time trends are included,

in particular in the upper tail, suggesting that in the pooled teachers sample the argument for a causal

relationship of basic skills test laws on student test scores is less strong than for subject test laws as

treated vs. untreated states appear to not be experiencing parallel output quality trends prior to changes

in basic skills test laws.

18

5.3 Heterogeneous effects of licensing on input quality for high vs. low-

income areas

The next question of interest is whether occupational licensing laws differentially affect areas of differing

income levels. Shapiro (1986) and Friedman and Friedman (1962) predict that licensing may result

in higher quality for high income consumers and lower quality for low income consumers. I test this

prediction by estimating (4). The results of this estimation for input quality are displayed in Table 5 and

Figure 6. First, Table 5 displays the results when the teacher testing law effect is evaluated at the mean of

the percent-free-lunch variable (i.e. δ + Iψ, where I is the mean of percent-free-lunch). Standard errors,

clustered at the state-year level, are reported in parentheses. In the pooled teacher sample, subject test

laws appear to have a positive impact of about 0.06 standard deviations, similar to the average effect

measured in Table 3 above. In the first-year teacher sample, in column 3, basic skills test laws appear to

have a large negative effect on the average teacher input quality, but this effect is only significant when

time trends are included. Other estimates appear relatively similar with or without time and experience

trends. As explained above, each of these regressions also includes the main effect of the percent free lunch

variable, not shown; the estimated coefficient on this main effect is significant and negative, implying

that teachers in lower-income areas tend to come from less-selective universities.

Figure 6 displays the estimated average effect of certification test laws on input quality evaluated at

each quantile of the percent-free-lunch variable. Note that, unlike the figures of distributional effects in

Sections 5.1 and 5.2, all of the points plotted in panels (a),(c), and (e) of Figure 6 come from the same

regression using first-year teachers, with the different estimates representing the effect of teacher testing

laws evaluated at different quantiles of the percent-free-lunch distribution. Similarly, all of the points

plotted in panels (b), (d), and (f) come from the a single regression using the pooled sample.

Figure 6 indicates that stricter occupational licensing laws are associated with an increase in teacher

qualifications, but only at the wealthiest school districts—those with a lower percentage of students who

qualify for free lunch. Panel (b) indicates that, among experienced teachers, at the 0.1 quantile of the

percent free lunch variable, subject tests are associated with an increase of nearly 0.15 standard deviations

in average teacher qualifications. This effect decreases as income decreases, as shown by movement to the

right on the horizontal axis. For the poorest districts shown, those at the 0.9 quantile, the point estimate

of the effect of subject test laws is negative (although insignificant). Panel (f) of Figure 6 demonstrates

that professional knowledge test laws have the same relationship as subject test laws, leading to increases

in teacher input quality in wealthier areas of approximately 0.07 standard deviations and a decrease of

similar magnitude for the lowest income districts. The remaining panels display a similar downward slope

but the relationship is imprecisely measured.

19

These results are consistent with the predictions of Shapiro (1986) and Friedman and Friedman (1962),

that any improvements in quality due to stricter licensing will accrue primarily to high-income areas at

the expense of low-income areas. One potential cause of this differential treatment effect would be that

stricter licensing is associated with higher wages and that schools in high-income areas are more capable

of increasing wages in response to changes in licensing and thus can continue to attract higher quality

teachers, as explored in Section 5.5 below. Another possibility is that higher quality teachers simply

prefer higher-income areas for a variety of reasons, as suggested by Boyd, Lankford, Loeb, and Wyckoff

(2005a,b). Regardless of the cause, these findings suggest a positive relationship between the impact of

licensing stringency and the wealth of the school district.

5.4 Heterogeneous effects of licensing on output quality for high vs. low-

income areas

The effect of licensing on student test scores for areas of differing income levels is displayed in Figure

7. A table analogous to Table 5 is omitted because the mean value of the percent free lunch variable is

not reported in the data; instead, the percent free lunch variable is reported in six bins. 90% confidence

intervals are displayed around each estimate, where standard errors are calculated by clustering at the

state-year level.

In Figure 7, the first-year teacher sample displays noisily measured effects, while the pooled sample

shows stronger patterns. For example, panel (a) does not display a significant effect of subject test laws

for the wealthiest schools, and displays a significant negative effect for schools in the second quartile of

income (26–50%). In the pooled sample, subject and basic skills test laws are associated with a larger

increase in test scores (0.05 standard deviations for subject test laws and 0.15 standard deviations for

basic skills test laws) for higher income districts. Appendix Figure A.3 focuses on the basic skills test

results and demonstrates that they are robust to the inclusion of trends.

In Figure 7, professional knowledge test laws display the opposite effect of basic skills test, with a

large and significant decrease of 0.15 standard deviations for the wealthiest districts. While the cause

of this opposite effect is unclear, it may be that the pedagogy skills required for these exams are more

valuable in low-income areas.

5.5 Substitution away from licensed professionals

Given the results reported thus far, it is natural to ask how, if at all, licensing induces consumers (in this

case, schools and school districts) to substitute away from licensed professionals. Previous studies (e.g.

20

Angrist and Guryan 2008 and others cited in Section 2) have demonstrated that more stringent licensing

requirements, including teacher certification tests, lead to higher wages. This is as theory would predict:

licensing requirements restrict supply and hence increase wages. If it is the case that higher income schools

are better equipped than lower income schools to raise wages in response to this restriction of supply,

lower income schools might be expected to respond to stricter occupational licensing by substituting

away from licensed professionals. Specifically, lower income schools could increase class sizes or hire more

emergency-certified teachers, i.e. those who did not have to pass certification tests. For example, Jepsen

and Rivkin (2009) found some evidence that lower income schools were less able to retain teachers during

supply shortages. The authors studied California’s 1996 law to reduce class sizes, finding that the law

led to a shortage of teachers. Many teachers left low-income schools to fill coveted vacancies at higher

income schools. Below I examine effects of certification testing on emergency-certified hirings, class sizes,

and wages in high vs. low-income areas.

To study whether teacher certification tests lead to larger increases in the use of emergency-certified

teachers in low-income areas than in high-income areas, I turn again to the SASS survey, which contains an

indicator for whether or not a given teacher was emergency certified. Summary statistics for this variable

as well as the other variables introduced in this section appear in Appendix Table A.1. Emergency

certified teachers do not meet the same testing requirements as other teachers and are hired when a

school is unable to meet staffing requirements using fully certified teachers. I estimate (4) with the

dependent variable replaced with the emergency-certified indicator. The results are displayed in the

first column of Figure 8. None of the results are significant, although for basic skills and professional

knowledge test laws the point estimates are increasing in the percent free lunch variable, consistent with

the idea of low-income areas being more likely than high income areas to increase the hiring of emergency

certified teachers in response to stricter occupational licensing.

I explore changes in class size in the second column of Figure 8, which displays the results of estimating

(4) with the dependent variable replaced by the pupil-to-teacher ratio as recorded in the Common Core

of Data (CCD) from the NCES, using all school districts in the database from the years 1988 to 2010.20

Panel (b) demonstrates that there is not a significant effect of subject test laws on class size. Panel

(d) indicates that there is a significant increase of approximately 0.25 in the student to teacher ratio at

the lowest-income school districts, those in which 80% or more qualify for free school lunch. At higher-

income schools, a marginally significant decrease in the pupil to teacher ratio of about 0.25 occurs. This is

consistent with the hypothesis that occupational licensing may lead to larger class sizes at these schools.

20I include the years 2009–2010 as well because, unlike the SASS and NAEP datasets, the CCD contains data for these

years, and my compiled certification test law data also contains these years. Years prior to 1988 are not available in the

CCD for the variables I study.

21

Professional knowledge tests, on the other hand, are associated with larger class sizes (an increase of

0.3-0.4 in the student to teacher ratio) at both high and low income schools.

Figure 9 demonstrates some weak evidence that basic skills test laws tend to increase wages primarily

in high income areas. The estimates in this figure come from (4) with the dependent variable replaced

by the log of teacher salary (in 2008 dollars) for teachers with a bachelor’s degree, as reported in the

SASS survey years. Panel (b) shows that, in higher-income schools, teacher salary increases with basic

skills test laws by approximately 2%. In lower-income schools, those with a higher percentage of students

qualifying for free lunch, the estimated increase is not statistically significant. The significant results

for basic skills test laws, however, were not robust to the inclusion of state time trends (not shown).

The results are difficult to interpret given that Figure 6 panel (d) showed that basic skills test laws did

not have a significant effect on teacher qualifications in areas varying by income. In panels (a) and (c),

estimates of the effects of subject and professional knowledge test laws are not significant. Note, however,

that these salary regressions use much less variation in licensing regimes, as salary data is only recorded

in survey years.

5.6 Event study

I now introduce an event study framework to test whether the observed changes in input and output

quality occurred after the changes in occupational licensing laws. This event study focuses solely on

subject test law changes because, as demonstrated in Table 1, few states eliminated the requirement of a

subject test for certification once this requirement was in place, making it simple to determine the year

in which the law change took place. Moreover, certification tests of subject matter have been the focus

of legislation (Kuenzi 2009).

For state s in year t, let d(−2)st be a dummy variable that is equal to 1 if year t was two years prior

to the year in which state s changed its subject test law. For one year prior to a law change, d(−1)st is

defined similarly. Let d(0)st be an indicator for whether state s changed its subject test law in year t. The

variables d(1)st , d

(2)st , d

(3)st , and d

(4+)st are dummies for year t being 1, 2, 3, or 4 or more years after state

s changed its law. If a state never instituted a subject test law, all of the dummies are set to zero. Let

the vector of these dummies be given by

dst = [d(−2)st d

(−1)st d

(0)st d

(1)st d

(2)st d

(3)st d

(4+)st ]′.

To estimate the effects of subject test laws on the distribution of teacher input quality in the framework

of this event study, I estimate (1) replacing the subject test dummy in the Lawst vector with the vector

of event dummies, dst. I modify the pooled regression model similarly.

22

The results are displayed in Appendix Figure A.4. I estimate nine regression, one regression for each

decile (τ = 0.1, 0.2, ...0.9), with each decile displayed in its own panel of Appendix Figure A.4. Only

the pooled teacher sample results are reported. Thus, the results in Appendix Figure A.4 are an event

study version of those in panel (b) of Figure 4. The results demonstrate that in the two years prior

to the law change, the effect is zero or insignificant at each quantile of input quality. In the year of

the law change and the two years immediately following the change, there is also no significant effect.

However, at three years and at four or more years after the law change, there is a significant, positive

effect on the distribution at many of the quantiles. This lends support to the evidence from Section 5.1,

which suggested that subject test laws raise the distribution of teacher input quality among experienced

teachers (demonstrating that the cause—the change in subject test law—appears to occur prior to the

effect—the change in the distribution of teacher qualifications). In particular, the principal effect of the

law change appears to occur several years after the law is first implemented. This phenomenon may arise

from announcements of law changes affecting decisions of undergraduates to enter the teaching occupation

or from a phase-in period or lag in effective enforcement of new certification laws.

Appendix Figure A.5 displays the same estimation but for output quality. That is, these results

can be compared with those in panel (b) of Figure 5. Recall that Figure 5 showed a positive impact

of 0.05 standard deviations at the 0.9 quantile for the pooled teachers sample, with insignificant results

at other quantiles. A similar pattern is seen in Appendix Figure A.5, with the 0.9 quantile, panel (i),

demonstrating a marginally significant effect, with the effect arriving at approximately two years after

the law change.

To apply this event study to the measurement of heterogeneous effects by income, I estimate (4) with

the subject test law dummy in the Lawst variable replaced by the event dummies, dst, and similarly for

the pooled sample model. I interact each of the event dummies with the percent free lunch variable. The

results of this estimation for the pooled sample are displayed in Appendix Figure A.6. Once again, at

most quantiles, no significant effects are measured prior to or coincident to the law change. Rather, the

effects appear to occur four or more years after the change takes place.

To examine the timing of the effects of subject test laws on output quality, I estimate (5) including

interactions of the percent free lunch dummies with the event study dummies in dst. The results are

displayed in Appendix Figure A.7. The effects of the subject law change are larger for the wealthier areas

(panels (a) and (b)), and these effects arrive mainly one and two years after the law change took place.

23

6 Conclusion

This study used state-level variation in teacher certification testing requirements over the period from

1983 to 2008 to examine how more stringent occupational licensing standards—in the form of teacher

certification tests prior to initial licensure—affect the composition of candidates who meet these standards

and enter the occupation (input quality, measured here by the selectivity of a teacher’s undergraduate

institution), and the distribution of the output in the profession (output quality, measured here by student

test scores). I found that subject area certification tests appear to raise the distribution of input quality

among teachers who remain in the occupation multiple years, but decrease the upper tail of input quality

among first-year teachers. The distribution of output quality appears to widen when certification test

laws are in place. I also found that increases in input or output quality due to stricter licensing accrue

primarily to high-income areas; low-income areas experience little or no benefit from stricter teacher

licensing requirements.

The results of this study suggest several avenues for future research. First, the empirical findings

can provide guidance for theoretical models of the how teacher certification exams affect outcomes. For

example, the results suggest that models of the process through which certification tests screen candidates

of different quality levels should take into account candidates’ heterogeneity in the costs of passing exams,

heterogeneity in outside career options, or heterogeneity in preferences for a teaching career. Given that

the effects of licensing differed for teachers who only remained in the profession for a short time period,

models should also consider heterogeneity in teachers’ propensity to exit the profession. Finally, the

results suggest a role for modeling theoretically the link between the effects of licensing on the quality

distribution and the effects of licensing on high vs. low income areas and how schools may compete to

attract high-quality teachers.

Although the focus of this study was on the teaching profession, the questions and approaches em-

ployed here can play a valuable role in the study of other occupations as well. In particular, the licensing

literature to date has focused on the effect of licensing on changes in average levels of quality, while

the stated purpose of licensing by many proponents is instead to provide a minimum level of quality

that candidates and services must meet. Future research could look for distributional effects in other

occupations, especially those in which consumer safety or asymmetric information of professionals vs.

consumers is a larger concern, such as medicine or law, to see if licensure laws do in fact prevent the

worst candidates from entering the occupation or prevent the worst outcomes from occurring.

Future research could also aid in determining the effects of occupational licensing on heterogeneous

consumers, examining whether these laws tend to harm low-income consumers relative to high-income

consumers. This study sheds some light on this question, as well as on how low-income areas may substi-

24

tute away from licensed professionals, indicating that policymakers may do well to consider potentially

unintended consequences of licensing on low-income areas. However, the question merits further research,

again particularly in professions providing services with a greater safety or informational concern, or in

occupations in which safety concerns are small, as licensing regulations in these occupations may be more

likely to result from professionals’ rent-seeking behavior.

25

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32

Figure 1: Illustration of possible changes to quality distribution

(a)

0

Teacher quality

Den

sity

→

(b)

Teacher quality

Den

sity

→

(c)

Teacher quality

Den

sity

←

(d)

Teacher quality

Den

sity

←

(e)

Teacher quality

Den

sity

→

(f)

Teacher quality

Den

sity

←

Notes: Figure illustrates potential effects of an increase in licensing stringency on the distribution of quality. Ineach panel licensing causes a shift from the red quality distribution to the blue quality distribution. Panels (a)and (b) both display an increase in average quality; in (a) this occurs through an improvement in the lower tailand in (b) through an improvement in the whole distribution. Panels (c) and (d) both display a decrease inaverage quality; in (c), this occurs through a decrease in the upper tail and in (d) through a decrease in thewhole distribution. Panels (e) and (f) display cases where the mean is unchanged but licensing tightens thedistribution in (e) and widens the distribution in (f).

33

Figure 2: Illustration of possible heterogeneous effects of licensing by income level

(a)

% free lunch

Effe

ct o

f lic

ensi

ng

(b)

% free lunch

Effe

ct o

f lic

ensi

ngNotes: Figure displays potential heterogeneous effects (the solid blue line) of licensing by income level relative toa constant average effect (the dashed red line). In (a), at higher income levels (lower percent free lunch), theeffects of licensing are larger and at lower income levels (higher percent free lunch) the effects of licensing aresmaller. In (b), at higher income levels (lower percent free lunch), the effects of licensing are smaller and atlower income levels (higher percent free lunch) the effects of licensing are larger.

Figure 3: Proportion of states requiring certification tests, 1983-2010.

.2.4

.6.8

1

1980 1990 2000 2010year

Subject test law Basic skills test lawProf knowledge test law

®

Notes: Figure displays (in blue) the proportion of states in each year which required teachers to pass a subjecttest prior to initial licensure. A similar measure is shown in red for basic skills test requirements and in greenfor professional knowledge test requirements.

34

Figure 4: Effects of certification test laws on input quality distribution

Notes: Effects of subject test law, basic skills test law, and professional knowledge test law on quantiles of teacher

input quality distribution. Panels on the left display first-year teacher sample and on the right display pooled

teacher sample. Robust, pointwise 90% confidence bands are displayed by dashed lines.

0.2 0.4 0.6 0.8-0.4

-0.2

0

0.2

Quantile of quality

First-year teachers sample

(a)

Subje

ct

test

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8-0.4

-0.2

0

0.2

Quantile of quality

(c)

Basic

skill

s t

est

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8-0.4

-0.2

0

0.2

Quantile of quality

(e)

Pro

f. k

now

ledge t

est

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8-0.4

-0.2

0

0.2

Quantile of quality

Pooled teachers sample

(b)

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8-0.4

-0.2

0

0.2

Quantile of quality

(d)

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8-0.4

-0.2

0

0.2

Quantile of quality

(f)

Avg u

nderg

rad S

AT

(std

)

35

Figure 5: Effects of certification test laws on output quality distribution

Notes: Effects of subject test law, basic skills test law, and professional knowledge test law on quantiles of output

quality distribution. Panels on the left display first-year teacher sample and on the right display pooled teacher

sample. Robust, pointwise 90% confidence bands are displayed by dashed lines.

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of quality

First-year teachers sample

(a)

Subje

ct

test

NA

EP

score

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of quality

(c)

Basic

skill

s t

est

NA

EP

score

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of quality

(e)

Pro

f. k

now

ledge t

est

NA

EP

score

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of quality

Pooled teachers sample

(b)

NA

EP

score

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of quality

(d)

NA

EP

score

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of quality

(f)

NA

EP

score

(std

)

36

Figure 6: Heterogeneous effects of certification test laws on input quality by income

Notes: Effects of subject test law, basic skills test law, and professional knowledge test law on teacher input quality

in areas differing by income, where income is measured by the percent of students eligible for free lunch. Panels on

the left display first-year teacher sample and on the right display pooled teacher sample. Robust, pointwise 90%

confidence bands are displayed by dashed lines.

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of % free lunch

First-year teachers sample

(a)

Subje

ct

test

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of % free lunch

(c)

Basic

skill

s t

est

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of % free lunch

(e)

Pro

f. k

now

ledge t

est

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of % free lunch

Pooled teachers sample

(b)

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of % free lunch

(d)

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8

-0.2

-0.1

0

0.1

0.2

Quantile of % free lunch

(f)

Avg u

nderg

rad S

AT

(std

)

37

Figure 7: Heterogeneous effects of certification test laws on output quality by income

Notes: Effects of subject test law, basic skills test law, and professional knowledge test law on teacher output

quality in areas differing by income, where income is measured by the percent of students eligible for free lunch.

Panels on the left display first-year teacher sample and on the right display pooled teacher sample. Robust,

pointwise 90% confidence bands are displayed by vertical lines.

-0.4

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

First-year teachers sample

(a)

Subje

ct

test

NA

EP

score

(std

)

-0.4

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(c)

Basic

skill

s t

est

NA

EP

score

(std

)

-0.4

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(e)

Pro

f. k

now

ledge t

est

NA

EP

score

(std

)

-0.4

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

Pooled teachers sample

(b)

NA

EP

score

(std

)

-0.4

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(d)

NA

EP

score

(std

)

-0.4

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(f)

NA

EP

score

(std

)

38

Figure 8: Heterogeneous effects of certification test laws on proportion of emergency-certified teachersand pupil-to-teacher ratio

Notes: Effects of subject test law, basic skills test law, and professional knowledge test law on proportion of

emergency certified teachers (observed in the SASS dataset) and pupil to teacher ratio (observed in the CCD) in

areas differing by income, where income is measured by the percent of students eligible for free lunch. Robust,

pointwise 90% confidence bands are displayed by dashed lines.

0.2 0.4 0.6 0.8

-0.1

-0.05

0

0.05

0.1

Quantile of % free lunch

Proportion emergency certified teachers

(a) Subject test law

0.2 0.4 0.6 0.8

-0.1

-0.05

0

0.05

0.1

Quantile of % free lunch

(c) Basic skills test law

0.2 0.4 0.6 0.8

-0.1

-0.05

0

0.05

0.1

Quantile of % free lunch

(e) Prof. knowledge test law

0.2 0.4 0.6 0.8-0.5

0

0.5

Quantile of % free lunch

Pupil to teacher ratio

(b) Subject test law

0.2 0.4 0.6 0.8-0.5

0

0.5

Quantile of % free lunch

(d) Basic skills test law

0.2 0.4 0.6 0.8-0.5

0

0.5

Quantile of % free lunch

(f) Prof. knowledge test law

39

Figure 9: Heterogeneous effects of certification test laws on log of teacher salary

Notes: Effects of subject test law, basic skills test law, and professional knowledge test law on teacher salary in

areas differing by income, where income is measured by the percent of students eligible for free lunch. Results

correspond to first-year teacher sample only. Robust, pointwise 90% confidence bands are displayed by dashed

lines.

0.2 0.4 0.6 0.8-0.05

0

0.05

Quantile of % free lunch

(a) Subject test law

0.2 0.4 0.6 0.8-0.05

0

0.05

Quantile of % free lunch

(b) Basic skills test law

0.2 0.4 0.6 0.8-0.05

0

0.05

Quantile of % free lunch

(c) Prof. knowledge test law

40

Table 1: Number of states changing certification test laws over the period 1983-2008.

Number of states Subject Basic skills

Prof

knowledge

With test law over whole sample

period

8 8 9

With no test law over whole

sample period

4 5 18

Changing from having no test law

to having a test law

39 34 23

Changing from having a test law

to not having a test law

2 13 9

Notes: Table displays, in the first column, the number of state which required a subject test for initial licensurein every year of the sample period, the number of states which never required a subject test during the sampleperiod, the number of states which changed from not requiring to requiring a subject test, and the number ofstates which changed from requiring to not requiring a subject test. The second and third columns show similarmeasures for basic skills and professional knowledge tests.

Table 2: Summary statistics of SASS and NAEP variables of interest

Mean

Standard

deviation Min Max

Teacher undergraduate

institution average SAT

915.98 106.65 570 1,410

Percent eligible for free lunch 39.11 24.17 0 100

Teacher years of experience 5.29 3.07 1 11

Cohort size 32.76 17.23 10 113

Eighth grade math scores 261.85 39.03 79.86 388.65

Teacher years of experience 4.54 2.58 1 11

Cohort size 203.00 106.76 10 1,439

SASS Variables (60,820 observations)

NAEP Variables (366,100 observations)

Notes: Summary statistics for SASS and NAEP datasets. In SASS dataset, cohort size represents the number ofteachers in a state/year/experience level cell. In NAEP dataset, cohort size represents the number of students ina cell taught by teachers in the same state/year/experience level.

41

Table 3: Average effect of certification test laws on input quality

(1) (2) (3) (4) (5) (6) (7) (8)

Subject test law -0.02 -0.04 -0.01 0.08*** 0.08*** 0.07*** 0.08*** 0.07***

(0.06) (0.06) (0.09) (0.02) (0.02) (0.03) (0.02) (0.03)

Basic skills test law -0.02 -0.02 -0.07 0.01 0.01 0.00 0.01 0.00

(0.04) (0.05) (0.07) (0.02) (0.02) (0.02) (0.02) (0.02)

Prof. knowledge test law 0.00 -0.01 -0.02 0.02 0.01 0.01 0.01 0.01

(0.05) (0.06) (0.08) -(0.02) -(0.02) -(0.02) -(0.02) -(0.02)

Demographic controls -- Yes Yes -- Yes Yes Yes Yes

State-specific time trend -- -- Yes -- -- Yes -- Yes

State-specific exp. effect -- -- -- -- -- -- Yes Yes

Sample Size

Dependent Variable: Average input quality within group

First-year teachers only All experience levels pooled

245 (state-year cells) 2,318 (state-year-cohort cells)

Notes: Table reports results from group-level quantile regressions of input quality on test law dummies. Anobservation is a group, which is a state-year cell in columns (1)–(3) and a state-year-cohort cell in columns(4)–(8). Dependent variable is the average input quality within a group, weighting by teacher sample weightswhen aggregating to the group level. Input quality at the individual teacher level is the average SAT for theteacher’s undergraduate institutional, standardized to have mean 0 and variance 1 in the sample. All regressionsinclude state and year fixed effects. All pooled regressions include experience cohort fixed effects. Robuststandard errors are reported in parentheses. ∗ = p < 0.10, ∗∗ = p < 0.05, ∗ ∗ ∗ = p < 0.01.

42

Table 4: Average effect of certification test laws on output quality

(1) (2) (3) (4) (5) (6) (7) (8)

Subject test law -0.05 -0.09* -0.06 0.02 0.00 0.00 0.01 0.01

(0.05) (0.05) (0.06) (0.03) (0.02) (0.02) (0.02) (0.03)

Basic skills test law 0.05 0.07* 0.03 0.06*** 0.04** 0.03* 0.05** 0.03

(0.04) (0.04) (0.06) (0.02) (0.02) (0.02) (0.02) (0.03)

Prof. knowledge test law 0.02 0.00 0.00 -0.02 -0.03 0.00 -0.04** 0.02

(0.07) (0.06) (0.05) (0.02) (0.02) (0.02) (0.02) (0.02)

Demographic controls -- Yes Yes -- Yes Yes Yes Yes

State-specific time trend -- -- Yes -- -- Yes -- Yes

State-specific exp. effect -- -- -- -- -- -- Yes Yes

Sample Size

Dependent Variable: Average output quality within group

First-year teachers only All experience levels pooled

259 (state-year cells) 2277 (state-year-cohort cells)

Notes: Table reports results from group-level quantile regressions of output quality on test law dummies. Anobservation is a group, which is a state-year cell in columns (1)–(3) and a state-year-cohort cell in columns(4)–(8). Dependent variable is the average output quality within a group, weighting by student sample weightswhen aggregating to the group level. Output quality at the individual student level is the eighth grade NAEPmath score, standardized to have mean 0 and variance 1 in the sample. All regressions include state and yearfixed effects. All pooled regressions include experience cohort fixed effects. Robust standard errors are reportedin parentheses. ∗ = p < 0.10, ∗∗ = p < 0.05, ∗ ∗ ∗ = p < 0.01.

43

Table 5: Average effect of certification test laws on input quality controlling for heterogeneous incomeeffects

(1) (2) (3) (4) (5) (6) (7) (8)

Subject test law -0.06 -0.06 0.01 0.06** 0.06** 0.05* 0.06** 0.05

(0.06) (0.06) (0.06) (0.03) (0.03) (0.03) (0.03) (0.03)

Basic skills test law -0.07 -0.08 -0.17** -0.03 -0.02 -0.03 -0.03 -0.04

(0.05) (0.05) (0.07) (0.02) (0.02) (0.02) (0.02) (0.03)

Prof. knowledge test law 0.00 -0.01 0.01 0.01 0.01 0.03 0.01 0.04

(0.06) (0.06) (0.07) (0.03) (0.03) (0.03) (0.03) (0.03)

Demographic controls -- Yes Yes -- Yes Yes Yes Yes

State-specific time trend -- -- Yes -- -- Yes -- Yes

State-specific exp. effect -- -- -- -- -- -- Yes Yes

Sample Size

Dependent Variable: Input quality

First-year teachers only All experience levels pooled

7,900 62,810

Notes: Table reports results from regressing input quality on certification test dummies and interaction ofcertification test dummies with percent of students qualifying for free lunch, evaluated at the mean of thepercent free lunch variable. An observation is a single teacher. Columns (1)–(3) use only first-year teachers;columns (4)–(8) use all experience levels. Input quality is the average SAT for the teacher’s undergraduateinstitutional, standardized to have mean 0 and variance 1 in the sample. All regressions include state and yearfixed effects and a main effect for the perfect free lunch, and are weighted by teacher sampling weights. Standarderrors, clustered at the state-year level, are reported in parentheses. ∗ = p < 0.10, ∗∗ = p < 0.05, ∗ ∗ ∗ = p < 0.01.

A Additional tables and figures

44

Table A.1: Summary statistics for SASS, NAEP, and CCD variables

Mean

Standard

deviation Min Max

District enrollment 67,771 204,023 0 1,197,117

Percent minority enrollment 35.59 29.37 0 100

Suburb dummy 0.47 -- -- --

Rurual dummy 0.25 -- -- --

Emergency certified dummy 0.13 0.34 0 1

Salary (2008 dollars) 27,674 7,395 11,800 51,400

Log salary (2008 dollars) 10.45 0.14 9.59 10.98

Pupil to teacher ratio 14.94 3.90 4.00 26.67

School percent black 16.03 23.57 0 100

School percent Hispanic 14.68 23.13 0 100

Encyclopedia in home dummy 0.61 Enrollement: 1-99 0.01

Suburb dummy 0.46 Enrollment: 100-299 0.07

Rural dummy 0.25 Enrollment: 300-499 0.18

Black dummy 0.17 Enrollment: 500-749 0.29

Hispanic dummy 0.15 Enrollment: 750-999 0.23

Asian dummy 0.04 Enrollment: 1000-1499 0.17

Male dummy 0.50 Enrollment: 1500+ students 0.05

SASS Variables (60,820 observations)

CCD Variables (328,810 observations)

NAEP Variables (366,100 observations)

NAEP Dummy Variables (means)

Notes: Summary statistics for variables not displayed in Table 2. Data on salaries and emergency certification

comes from the SASS sample of first-year teachers, and consists of 8,770 observations. Data on pupil to teacher

ratios comes from the CCD from 1988-2010.

45

Figure A.1: Trend robustness of input quality distributional effects

Notes: Effects of subject test law on distribution of input quality with pooled teacher sample, with state-specific

linear time trends and/or state-specific returns to teaching experience included.

0.2 0.4 0.6 0.8-0.05

0

0.05

0.1

0.15

Quantile of quality

(a) State time trendsA

vg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8-0.05

0

0.05

0.1

0.15

Quantile of quality

(b) State experience trends

Avg u

nderg

rad S

AT

(std

)

0.2 0.4 0.6 0.8-0.05

0

0.05

0.1

0.15

Quantile of quality

(c) State time and experience trends

Avg u

nderg

rad S

AT

(std

)

46

Figure A.2: Trend robustness of output quality distributional effects

Notes: Effects of subject test law on distribution of output quality with pooled teacher sample, with state-specific

linear time trends and/or state-specific returns to teaching experience included.

0.2 0.4 0.6 0.8-0.1

-0.05

0

0.05

0.1

Quantile of quality

Subject test law

(a) State time trends

NA

EP

score

(std

)

0.2 0.4 0.6 0.8-0.1

-0.05

0

0.05

0.1

Quantile of quality

(c) State experience trends

NA

EP

score

(std

)

0.2 0.4 0.6 0.8-0.1

-0.05

0

0.05

0.1

Quantile of quality

(e) State time and experience trends

NA

EP

score

(std

)

0.2 0.4 0.6 0.8-0.1

-0.05

0

0.05

0.1

Quantile of quality

Basic skills test law

(b) State time trends

NA

EP

score

(std

)

0.2 0.4 0.6 0.8-0.1

-0.05

0

0.05

0.1

Quantile of quality

(d) State experience trends

NA

EP

score

(std

)

0.2 0.4 0.6 0.8-0.1

-0.05

0

0.05

0.1

Quantile of quality

(f) State time and experience trends

NA

EP

score

(std

)

47

Figure A.3: Trend robustness of output quality effects by income level

Notes: Effects of basic skills test law on output quality by bins of percent free lunch distribution using pooled

teacher sample, with state-specific linear time trends and/or state-specific returns to teaching experience included.

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

Subject test law

(a) State time trends

NA

EP

score

(std

)

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(c) State experience trends

NA

EP

score

(std

)

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(e) State time and experience trends

NA

EP

score

(std

)

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

Basic skills test law

(b) State time trends

NA

EP

score

(std

)

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(d) State experience trends

NA

EP

score

(std

)

-0.2

0

0.2

Percent free lunch

0-5%

6-10

%

11-2

5%

26-5

0%

51-7

5%

76-1

00%

(f) State time and experience trends

NA

EP

score

(std

)

48

Fig

ure

A.4

:E

vent

stu

dy:

effec

tof

sub

ject

test

law

son

inp

ut

qu

ali

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ich c

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(-2)

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-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

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law

change

(a)

0.1

quantile

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Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

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subje

ct

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law

change

(b)

0.2

quantile

of qualit

y

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(c)

0.3

quantile

of qualit

y

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(d)

0.4

quantile

of qualit

y

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(e)

0.5

quantile

of qualit

y

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(f)

0.6

quantile

of qualit

y

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(g)

0.7

quantile

of qualit

y

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(h)

0.8

quantile

of qualit

y

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(i)

0.9

quantile

of qualit

y

Avg undergrad SAT (std)

49

Fig

ure

A.5

:E

vent

stu

dy:

effec

tof

sub

ject

test

law

son

ou

tpu

tqu

ali

tyd

istr

ibu

tion

N

ote

s: E

ven

t st

ud

y a

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f su

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est

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on q

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les

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her

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ity d

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tes

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ect

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, th

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lot

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esp

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50

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5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(a)

0.1

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(b)

0.2

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(c)

0.3

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(d)

0.4

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(e)

0.5

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(f)

0.6

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(g)

0.7

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(h)

0.8

quantile

of qualit

y

NAEP score (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.1

-0.0

50

0.0

5

0.1

Years

befo

re/a

fter

subje

ct

test

law

change

(i)

0.9

quantile

of qualit

y

NAEP score (std)

50

Fig

ure

A.6

:E

vent

stu

dy:

het

erogen

eou

seff

ects

of

sub

ject

test

law

son

inp

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t fo

r a

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lar

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ile

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ent

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aria

ble

. W

ith

in a

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en p

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(>=

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-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(a)

0.1

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(b)

0.2

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(c)

0.3

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(d)

0.4

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(e)

0.5

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(f)

0.6

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(g)

0.7

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(h)

0.8

quantile

% fre

e lunch

Avg undergrad SAT (std)

(-2)

(-1)

(0)

(+1)

(+2)

(+3)

(>=

4)

-0.2

-0.10

0.1

0.2

Years

befo

re/a

fter

subje

ct

test

law

change

(i)

0.9

quantile

% fre

e lunch

Avg undergrad SAT (std)

51

Figure A.7: Event study: heterogeneous effects of subject test laws on output quality by income

Notes: Event study analysis of subject test law on teacher output quality in areas differing by income and using

only states which changed from having no subject test law to having a subject test law. Each panel displays the

effect for a particular bin of the percent free lunch variable. Within a given panel, the plot corresponds to the effect

two years before the subject test law changed, one year before, the year of the change, one year after, etc. The final

point corresponds to the effect four or more years after. Robust, pointwise 90% confidence bands are displayed by

dashed lines.

(-2) (-1) (0) (+1) (+2) (+3) (>=4)

-0.2

0

0.2

0.4

Years before/after subject test law change

(a) 0-5% free lunch

NA

EP

score

(std

)

(-2) (-1) (0) (+1) (+2) (+3) (>=4)

-0.2

0

0.2

0.4

Years before/after subject test law change

(b) 6-10% free lunch

NA

EP

score

(std

)

(-2) (-1) (0) (+1) (+2) (+3) (>=4)

-0.2

0

0.2

0.4

Years before/after subject test law change

(c) 11-25% free lunch

NA

EP

score

(std

)

(-2) (-1) (0) (+1) (+2) (+3) (>=4)

-0.2

0

0.2

0.4

Years before/after subject test law change

(d) 26-50% free lunch

NA

EP

score

(std

)

(-2) (-1) (0) (+1) (+2) (+3) (>=4)

-0.2

0

0.2

0.4

Years before/after subject test law change

(e) 51-75% free lunch

NA

EP

score

(std

)

(-2) (-1) (0) (+1) (+2) (+3) (>=4)

-0.2

0

0.2

0.4

Years before/after subject test law change

(f) 76-100% free lunch

NA

EP

score

(std

)

52